A Bayesian Multi-Model Inference Method for Reliability Analysis Considering Vine Structure Uncertainty Under Limited Data

This paper investigates the epistemic uncertainty associated with dependence modeling and its impact on structural reliability analysis when data for vine structure selection is limited. Conventionally, the vine copula model characterizing dependent input variables in reliability analysis is typically assumed to be either a single model or the optimal fit model obtained from the data. However, subjective assumptions and data scarcity may introduce bias into correlation measurements, causing significant deviations between the vine structure and the actual dependence structure, as well as substantial errors in reliability analysis. In this paper, we address model uncertainties in vine structures arising from sparse data by introducing Bayesian multi-model inference. This approach identifies the corresponding Bayesian posterior probabilities for an ensemble of candidate vine structures based on their overall dependence modeling performance. Utilizing the Bayes factor to screen effective candidate vine structures, a reweighted model set is formed to quantify model uncertainty in dependence modeling. The integrated first-order reliability method for regular vine copulas provides both precision and high efficiency in reliability analysis. Finally, numerical and engineering examples demonstrate that the proposed method yields more accurate and robust reliability analysis results across various sample sizes in contrast to a single optimal vine copula model.